def diagrammatic_to_sentential(context, F, named_states,
attribute_interpretation, variable_assignment,
*formulae):
"""
Verify that on the basis of the present diagram :math:`(\sigma;\\rho)` of
the Context object :math:`(\\beta;(\sigma;\\rho))` in the ``context``
parameter and some set of Formula objects
:math:`F_{1}, \ldots, F_{k}, k \ge 0` provided as optional positional
arguments in the ``formulae`` parameter, that for each NamedState object
:math:`(\sigma_{1}; \\rho_{1}), \ldots,(\sigma_{n}; \\rho_{n}), n > 0`,
contained in the ``named_states`` parameter, a Formula object :math:`F`
provided in the ``F`` parameter can be derived in every one of these
:math:`n` cases.
This is rule :math:`[C_{3}]`.
This function works as follows:
1. If :math:`k > 0` (i.e., if at least one Formula object is provided as an
optional positional argument to the ``formulae`` parameter), compute the
basis :math:`\mathcal{B}(F_{1}, \\rho, \chi) ~ \cup ~ \cdots ~ \cup ~ \
\mathcal{B}(F_{k}, \\rho, \chi)` of :math:`F_{1}, \ldots, F_{k}` and
determine if the NamedState objects
:math:`(\sigma_{1}; \\rho_{1}), \ldots,(\sigma_{n}; \\rho_{n})`
provided in the ``named_states`` parameter form an exhuastive set of
possibilities on this basis.
2. Determine if the proviso
:math:`(\sigma;\\rho) \\Vvdash_{\{F_{1}, \ldots, F_{k}\}} \
\{(\sigma_{1}; \\rho_{1}), \ldots,(\sigma_{n}; \\rho_{n})\}` (where
:math:`k \ge 0`) holds.
3. Return the evaluation of
:math:`(\\beta \cup \{F_{1}, \ldots, F_{k}\};(\sigma;\\rho)) \models F`.
:param context: The Context object :math:`(\\beta;(\sigma;\\rho))` from \
which the present diagram :math:`(\sigma;\\rho)` comes from.
:type context: Context
:param F: The Formula object :math:`F` derivable in the :math:`n > 0` \
cases provided by the NamedState objects \
:math:`(\sigma_{1}; \\rho_{1}), \ldots,(\sigma_{n}; \\rho_{n})` in the \
``named_state`` parameter.
:type F: Formula
:param named_states: The NamedState objects \
:math:`(\sigma_{1}; \\rho_{1}), \ldots,(\sigma_{n}; \\rho_{n}), n > 0` \
functioning as the set of :math:`n` exhaustive cases from which :math:`F` \
can be derived.
:type named_states: ``list``
:param attribute_interpretation: The AttributeInterpretation object \
:math:`I` to use for the interpretation of truth values and the \
computation of the basis of :math:`F_{1}, \ldots, F_{k}`.
:type attribute_interpretation: AttributeInterpretation
:param variable_assignment: The VariableAssignment object :math:`\chi` to \
consider when computing the basis \
:math:`\mathcal{B}(F_{1}, \\rho, \chi) ~ \cup ~ \cdots ~ \cup ~ \
\mathcal{B}(F_{k}, \\rho, \chi)` of :math:`F_{1}, \ldots, F_{k}` or \
``None`` if all terms of the :math:`F_{1}, \ldots, F_{k}` are in \
:math:`\\rho`.
:type variable_assignment: VariableAssignment | ``None``
:param formulae: The :math:`{k \ge 0}` Formula objects \
:math:`F_{1}, \ldots, F_{k}` to use in the computation of the basis, \
computation of the proviso and the evaluation of \
:math:`{(\\beta \cup \{F_{1}, \ldots, F_{k}\};(\sigma;\\rho)) \models F}`.
:type formulae: Formula
:return: The result of the evaluation of \
:math:`(\\beta \cup \{F_{1}, \ldots, F_{k}\};(\sigma;\\rho)) \models F`.
:rtype: ``bool``
:raises ValueError: If :math:`{k > 0}`, the NamedState objects \
:math:`{(\sigma_{1}; \\rho_{1}), \ldots,(\sigma_{n}; \\rho_{n}), n > 0}` \
are not exhaustive on the basis of the Formula objects \
:math:`F_{1}, \ldots, F_{k}` or the proviso \
:math:`{(\sigma;\\rho) \\Vvdash_{\{F_{1}, \ldots, F_{k}\}} \
\{(\sigma_{1}; \\rho_{1}), \ldots,(\sigma_{n}; \\rho_{n})\}}` (where \
:math:`k \ge 0`) does not hold.
"""
if formulae:
constant_assignment = context._named_state._p
basis = Formula.get_basis(constant_assignment, variable_assignment,
attribute_interpretation, *formulae)
if not context._named_state.is_exhaustive(basis, *named_states):
raise ValueError(
"named states are not exahustive on basis of formulae.")
assumption_base = AssumptionBase(*formulae)
else:
assumption_base = AssumptionBase(context._assumption_base._vocabulary)
proviso = context._named_state.is_named_entailment(
assumption_base, attribute_interpretation, *named_states)
if not proviso:
raise ValueError("[C3] proviso does not hold")
formulae_union = context._assumption_base._formulae + list(formulae)
if formulae_union:
assumption_base_union = AssumptionBase(*formulae_union)
else:
assumption_base_union = AssumptionBase(
context._assumption_base._vocabulary)
# Determine if (β ∪ {F1,...,Fk}; (σ; ρ)) |= F; proviso holds at this point
extended_context = Context(assumption_base_union, context._named_state)
if extended_context.entails_formula(F, attribute_interpretation):
return True
else:
return False
def diagrammatic_to_sentential(context, F, named_states, attribute_interpretation, variable_assignment, *formulae):
"""
Verify that on the basis of the present diagram :math:`(\sigma;\\rho)` of
the Context object :math:`(\\beta;(\sigma;\\rho))` in the ``context``
parameter and some set of Formula objects
:math:`F_{1}, \ldots, F_{k}, k \ge 0` provided as optional positional
arguments in the ``formulae`` parameter, that for each NamedState object
:math:`(\sigma_{1}; \\rho_{1}), \ldots,(\sigma_{n}; \\rho_{n}), n > 0`,
contained in the ``named_states`` parameter, a Formula object :math:`F`
provided in the ``F`` parameter can be derived in every one of these
:math:`n` cases.
This is rule :math:`[C_{3}]`.
This function works as follows:
1. If :math:`k > 0` (i.e., if at least one Formula object is provided as an
optional positional argument to the ``formulae`` parameter), compute the
basis :math:`\mathcal{B}(F_{1}, \\rho, \chi) ~ \cup ~ \cdots ~ \cup ~ \
\mathcal{B}(F_{k}, \\rho, \chi)` of :math:`F_{1}, \ldots, F_{k}` and
determine if the NamedState objects
:math:`(\sigma_{1}; \\rho_{1}), \ldots,(\sigma_{n}; \\rho_{n})`
provided in the ``named_states`` parameter form an exhuastive set of
possibilities on this basis.
2. Determine if the proviso
:math:`(\sigma;\\rho) \\Vvdash_{\{F_{1}, \ldots, F_{k}\}} \
\{(\sigma_{1}; \\rho_{1}), \ldots,(\sigma_{n}; \\rho_{n})\}` (where
:math:`k \ge 0`) holds.
3. Return the evaluation of
:math:`(\\beta \cup \{F_{1}, \ldots, F_{k}\};(\sigma;\\rho)) \models F`.
:param context: The Context object :math:`(\\beta;(\sigma;\\rho))` from \
which the present diagram :math:`(\sigma;\\rho)` comes from.
:type context: Context
:param F: The Formula object :math:`F` derivable in the :math:`n > 0` \
cases provided by the NamedState objects \
:math:`(\sigma_{1}; \\rho_{1}), \ldots,(\sigma_{n}; \\rho_{n})` in the \
``named_state`` parameter.
:type F: Formula
:param named_states: The NamedState objects \
:math:`(\sigma_{1}; \\rho_{1}), \ldots,(\sigma_{n}; \\rho_{n}), n > 0` \
functioning as the set of :math:`n` exhaustive cases from which :math:`F` \
can be derived.
:type named_states: ``list``
:param attribute_interpretation: The AttributeInterpretation object \
:math:`I` to use for the interpretation of truth values and the \
computation of the basis of :math:`F_{1}, \ldots, F_{k}`.
:type attribute_interpretation: AttributeInterpretation
:param variable_assignment: The VariableAssignment object :math:`\chi` to \
consider when computing the basis \
:math:`\mathcal{B}(F_{1}, \\rho, \chi) ~ \cup ~ \cdots ~ \cup ~ \
\mathcal{B}(F_{k}, \\rho, \chi)` of :math:`F_{1}, \ldots, F_{k}` or \
``None`` if all terms of the :math:`F_{1}, \ldots, F_{k}` are in \
:math:`\\rho`.
:type variable_assignment: VariableAssignment | ``None``
:param formulae: The :math:`{k \ge 0}` Formula objects \
:math:`F_{1}, \ldots, F_{k}` to use in the computation of the basis, \
computation of the proviso and the evaluation of \
:math:`{(\\beta \cup \{F_{1}, \ldots, F_{k}\};(\sigma;\\rho)) \models F}`.
:type formulae: Formula
:return: The result of the evaluation of \
:math:`(\\beta \cup \{F_{1}, \ldots, F_{k}\};(\sigma;\\rho)) \models F`.
:rtype: ``bool``
:raises ValueError: If :math:`{k > 0}`, the NamedState objects \
:math:`{(\sigma_{1}; \\rho_{1}), \ldots,(\sigma_{n}; \\rho_{n}), n > 0}` \
are not exhaustive on the basis of the Formula objects \
:math:`F_{1}, \ldots, F_{k}` or the proviso \
:math:`{(\sigma;\\rho) \\Vvdash_{\{F_{1}, \ldots, F_{k}\}} \
\{(\sigma_{1}; \\rho_{1}), \ldots,(\sigma_{n}; \\rho_{n})\}}` (where \
:math:`k \ge 0`) does not hold.
"""
if formulae:
constant_assignment = context._named_state._p
basis = Formula.get_basis(constant_assignment, variable_assignment, attribute_interpretation, *formulae)
if not context._named_state.is_exhaustive(basis, *named_states):
raise ValueError("named states are not exahustive on basis of formulae.")
assumption_base = AssumptionBase(*formulae)
else:
assumption_base = AssumptionBase(context._assumption_base._vocabulary)
proviso = context._named_state.is_named_entailment(assumption_base, attribute_interpretation, *named_states)
if not proviso:
raise ValueError("[C3] proviso does not hold")
formulae_union = context._assumption_base._formulae + list(formulae)
if formulae_union:
assumption_base_union = AssumptionBase(*formulae_union)
else:
assumption_base_union = AssumptionBase(context._assumption_base._vocabulary)
# Determine if (β ∪ {F1,...,Fk}; (σ; ρ)) |= F; proviso holds at this point
extended_context = Context(assumption_base_union, context._named_state)
if extended_context.entails_formula(F, attribute_interpretation):
return True
else:
return False
